Tuesday, September 28, 2010

Ionic Rhombic Dodecahedron and Cuboctahedron

Here is my latest beaded bead using my Ionic Polyhedra weave. This one is based upon the rhombic dodecahedron. It is 33 mm wide and composed of over 600 beads. I am happy with the way it came out because it is reasonably stiff and very hollow. Because it is so hollow and the holes are so large, my boyfriend says it looks like a geode. I like the way you can see all the way through 4 different holes simultaniously. The first photo shows this.

The second photo shows a different type of hole in this beaded bead.

After I took these photos, I found another way to hold it that shows two holes. In this view below, the large purple crystals in the back show through the holes in the front, falsely making the beaded bead appear solid.

The rhombic dodecahedron is the dual of the cuboctahedron. Below I show the dual correspondence between these two polyhedra, using my Mini Ionic Polyhedra weave. I tried to pose the pair of beaded beads so that little gold beads have the same configuration in each photo.

The cuboctahedron is on the left and the rhombic dodecahedron is on the right. Because they are duals of one another, one has faces where the other has corners. In terms of beaded beads, one has holes where the other has stars of seed beads.

These two little beaded beads are just two centimeters wide, and they are each composed of exactly 288 beads.

Ooo yummy! The ionic rhombic dodecahedron looks like a rounded octahedron in the first photo (which is what happened when I tried to fold this polyhedron out of origami paper, many years ago), but it looks much rounder in the other photos... Is it more round? Or are my eyes playing tricks on me?

Love the color combos and distributions in the mini ionics. It really helps to visualize the duality.

I guess the rhombic dodecahedron is round, but it has really big holes, so it's hard to say. Because it has cuboctahedral symmetry, it's rounder than say, the antiprism or the pentacluster.

I'm glad you can make out the duality in the photos. I thought it was pretty cool seeing the two beaded beads together. I had to remake the inside of the second one twice so I could get the coloring to match just so.